You can start with this top 10 list. The major attraction here is Damien Hirst - you have until 9 September to see the famous shark in formaldehyde if you haven't already - but as you will see there is a lot going on. I would choose the Da Vinci exhibition myself.

Another really interesting small show is Grayson Perry's The Vanity of Small Differences which is on until 11 August, so you would have to be quick. This consists just of a series of tapestries exploring British culture and especially the class system.

For a more general view of what's going on, you could try the visit London website. If you narrow your search you can look for what really interests you, and you might also find other interesting things going on like dance, music, theatre etc. Whatever you choose, have a great time - London is supposed to be quite quiet while the Olympics are on, so this is a good time to go.